The implementation of the linear covariant gauge on the lattice faces a conceptual problem: using the standard compact discretization, the gluon field is bounded, while the four-divergence of the gluon field satisfies a Gaussian distribution, i.e. it is unbounded. This can give rise to convergence problems when a numerical implementation is attempted. In order to overcome this problem, one can use different discretizations for the gluon field or consider an SU(N c ) group with sufficiently large N c . One can also consider small values of the gauge parameter ξ and study numerically the limiting case of ξ → 0, i.e. the Landau gauge. These different approaches will be discussed here.

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